Our work yields an upper bound on the metric dimension of random \(\Delta \) -regular graphs.
The metric dimension problem was first introduced by Slater [1]} and Harary and Melter [2]}, see also [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
The metric dimension of a graph is the cardinality of a smallest subset \(S\)  of vertices such that every vertex in the graph has a unique vector of distances to the vertices in \(S\) .
On regular graphs, the metric dimension problem was studied in special cases [5]}, [12]}.
In Erdös-Rényi random graphs, the metric dimension problem was studied by Bollobás, Mitsche, and Prałat [13]}.
Mitsche and Rué [14]} also considered the random forest model.
